Surface Reconstruction From Unorganized Points Of Arbitrary Topology With Bi-quadratic Spline Surface

Reverse engineering, a new kind of industrial processing and manufacturing technology, hasbeen national attention. Surface reconstruction is a key technology in reverse engineering, whichaims to achieve the mathematical expression of geometric model for complex free-form surfacefrom the scattered measured data. Although a lot of literature have explored the problem of surfacereconstruction, but it need to be studied deeply on that reconstructing surface from unorganizedpoints of arbitrary topology.This article aims to explore and study this issue. In this paper, we present an algorithm andsystem for converting dense irregular polygon meshes of arbitrary topology intoG~1surface bybiquartic spline surface.The article main focus on:1. It discusses some commonly used parameterization methods and presents the base surfaceparameterization, a simple technique to assign parameter values to randomly measured pointsfor the least squares fitting of biquartic spline surface. It describes the basic idea of the basesurface parameterization. It gives different methods for constructing the base surface and themethod for projecting the measured points to the base surface.2. It presents an efficient method for fitting aG~1surface of arbitrary topological type tounorganized points by biquartic spline surface. First, it gains triangular mesh surface fromunorganized points; Second, it gives the idea of data segmentation, by which the triangularmesh surface is divided into polygonal patches. Third, it introduces a scheme for adaptiverefinement of the polygonal patches to obtain a refined mesh of quadrilateral subcells, thencompute the relational matrix between global control points and Bézier coefficients. Finally,construct the biquartic spline surface patch network on quadrilateral domain maintainingG~1continuity between patches.3. It presents a multi-step iterative algorithm of least squares surface approximation to scattereddata using biquartic spline surface. First, make use of the base surface parameterization to getthe initial parameter values. Then, solve the normal equation, where choosing energy functionas the smooth constraints, to obtain the first fitting surface. Finally, make use of multi-stepiterative algorithm to obtain the final smooth fitting surface...